Marginal Stability of the Convective Boundary Layer

We hypothesize that the convective atmospheric boundary layer is marginally stable when the damping effects of turbulence are taken into account. If the effects of turbulence are modeled as an eddy viscosity and diffusivity, then an idealized analysis based on the hypothesis predicts a well-known scaling for the magnitude of the eddy viscosity and diffusivity. It also predicts that the marginally stable modes should have vertical and horizontal scales comparable to the boundary layer depth. A more quantitative numerical linear stability analysis is presented for a realistic convective boundary layer potential temperature profile and is found to support the hypothesis.